2. Which of the following functions translates the graph of the parent function f(x) = x 2 horizontally left 8 units? Circle one. A h(x) = x² + 8 C (x) = x² – 8 B h(x) = (x – 8)2 D h(x) = (x + 8)² %3D

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 2: Translating the Graph of a Function**

Consider the following question regarding the translation of the function.

**Question:**
Which of the following functions translates the graph of the parent function \( f(x) = x^2 \) horizontally left 8 units? **Circle one.**

**Options:**

**A.** \( h(x) = x^2 + 8 \)  
**B.** \( h(x) = (x - 8)^2 \)  
**C.** \( h(x) = x^2 - 8 \)  
**D.** \( h(x) = (x + 8)^2 \)  

**Explanation:**
To translate the function \( f(x) = x^2 \) horizontally to the left, we use the transformation \( x \rightarrow x + k \), where \( k \) is the number of units to move. Thus, translating left by 8 units involves replacing \( x \) with \( x + 8 \).

Therefore, the correct function is \( h(x) = (x + 8)^2 \), which is option **D**.
Transcribed Image Text:**Question 2: Translating the Graph of a Function** Consider the following question regarding the translation of the function. **Question:** Which of the following functions translates the graph of the parent function \( f(x) = x^2 \) horizontally left 8 units? **Circle one.** **Options:** **A.** \( h(x) = x^2 + 8 \) **B.** \( h(x) = (x - 8)^2 \) **C.** \( h(x) = x^2 - 8 \) **D.** \( h(x) = (x + 8)^2 \) **Explanation:** To translate the function \( f(x) = x^2 \) horizontally to the left, we use the transformation \( x \rightarrow x + k \), where \( k \) is the number of units to move. Thus, translating left by 8 units involves replacing \( x \) with \( x + 8 \). Therefore, the correct function is \( h(x) = (x + 8)^2 \), which is option **D**.
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